Giuseppe Di Maio, Enrico Meccariello, Somashekhar Naimpally
Symmetric Proximal Hypertopology
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 58, 3-25(2004)

MSC:

54B20 Hyperspaces

54E05 Proximity structures and generalizations

54E15 Uniform structures and generalizations

54E35 Metric spaces, metrizability

Abstract: In 1988 a new hypertopology, called \textbf{proximal
(finite) hypertopology} was discovered. It involves the use of a proximity
in the upper part but leaves the lower part the same as the lower Vietoris
topology. In 1966, the lower Vietoris topology, which involves finitely many
open sets, led to another lower topology involving locally finite families
of open sets. In this paper, we change the lower hypertopology using a
proximity and thus get a ``symmetric`` proximal hypertopology, which
includes the earlier `finite' topologies.
Keywords: Proximities, hyperspace, lower proximal hypertopology, upper proximal hypertopology, symmetric proximal hypertopology, Bombay hypertopology
Notes: Dedicated to our friend Professor Dr. Harry Poppe on his 70$^{th}$ birthday.